Decadal climate predictions have gained importance in recent years for their potential added value for decision making in economy and society (e.g., ). There is an increasing body of literature focusing on skilful decadal predictions for Europe, not only regarding basic variables but also for extremes and user-oriented variables . Atlantic Multidecadal Variability (AMV) – characterised by low frequency variability of North Atlantic sea surface temperatures – has been found to be highly predictable on decadal timescales and is known to play a role in European summer climate . Positive AMV phase sea-surface temperature (SST) signals include a warmer North Atlantic subpolar gyre (SPG), and – lagging behind the SPG response – a band of warm SSTs in the tropical North Atlantic (and similar but opposite during the negative phase; ). This characteristic pattern of AMV SST anomalies is sometimes referred to as the “horseshoe” pattern.

Whilst initialised climate prediction for the wintertime North Atlantic-Europe (NAE) sector has proven skilful on a range of timescales (e.g. ), summer prediction skill remains more elusive, but with episodic “windows of opportunity” for skilful predictions under certain conditions (e.g. ). The increasing risk of extreme heat in Europe during summer due to anthropogenic influence means that predictions of summer climate are particularly relevant , especially if dynamically-driven variability exacerbates the externally forced trend. As a result, it is important to understand the impacts of relevant predictable drivers such as AMV, as well as the present capability of models in simulating them.

The atmospheric response to diabatic heating in the extratropics, such as the heating associated with the SPG component of AMV, is a shallow cyclonic circulation one quarter-wavelength downstream of the heating, which acts to cool the heating region . This diabatic heating response to AMV has been found to be robust and leads to increased surface temperatures in central Europe by advecting warm air polewards . AMV-associated tropical SST anomalies lead to upper level divergence anomalies and hence a source of Rossby waves which can propagate to the extratropical NAE sector . This Rossby wave response has been associated with increased temperatures in Europe .

The tropical and extratropical SST components of AMV are strongly coupled on decadal timescales and therefore so are their impacts . The time period (the last ∼45–70 years) for which high quality observational data, particularly for non-surface fields, exists is short relative to the multidecadal timescale of AMV and therefore it can be difficult to separate the tropical and extratropical contributions to AMV impacts using observations or reanalyses alone. Large ensembles of model simulations (e.g. ) allow for a larger sample of AMV variability and resulting European climate impacts. Furthermore, skilful predictions of NAE sector atmospheric variability require large ensembles, to not only separate the predictable “signal” and unpredictable “noise” variability which exist in reality, but also as prediction systems tend to underestimate the signal-to-noise ratio in the NAE region . This issue is known as the “signal-to-noise paradox” due to the counterintuitive consequence that the correlation skill between the ensemble mean and observations is higher than the average correlation between the ensemble mean and individual members , and there is evidence of its presence during boreal summer . Using a single model large ensemble prediction system ensures that differences between members are result of chaotic “noise” variability rather than model differences, avoiding the risk of a reduced signal-to-noise ratio arising from inter-model spread .

The aim of this study is to understand the capability of a large single model ensemble decadal hindcast in predicting the summertime atmospheric circulation response to AMV. In particular, the separate roles of two distinct atmospheric responses to AMV are investigated: one associated with diabatic heating due to subpolar SST anomalies, and another associated with the upper tropospheric response to tropical SST anomalies, resulting in a source of Rossby waves. The data and methodology used in this study are presented in Sect. . AMV SSTs and the associated atmospheric response on 7 year timescales are analysed and compared in observations/reanalyses and model experiments in Sect. . Section  examines the timescale dependence of the upper tropospheric response. Section  summarises and contextualises the results of this study.

This study uses an 80 member decadal hindcast ensemble using the low resolution version of the Max-Planck-Institute for Meteorology (MPI) Earth System Model (MPI-ESM-LR; ), which uses a grid spacing of approximately 200 km in the atmosphere and 150 km in the ocean. The ensemble consists of an original 16 member ensemble and a more recent addition of 64 further members . Members are initialised every year in November from 1960 to 2019 inclusive; the ocean is initialised using temperature and salinity from the EN4 ocean reanalysis to create a 16 member ensemble Kalman filter assimilation, whilst the atmosphere is nudged to reanalysis, with perturbations applied to the stratosphere to generate 4 extra members per each assimilation member, resulting in a total of 5×16=80 members. Further details can be found in . All members are run for at least 10 full calendar years beyond the initialisation date, and the original 16 members have been extended to 20 years . Whilst a higher resolution configuration of the MPI-ESM decadal prediction system exists , the lower resolution used here facilitated the production of both the increased ensemble size and the extended length runs. Lead year 1–7 means are used except where otherwise stated; this is similar to other studies focused on decadal variability of mid-latitude atmospheric circulation (e.g. ). Throughout the study, any averaging of multiple years in the hindcasts is done by taking different leads from the same initialisation, rather than averaging over different initialisations at the same lead. 50 historical runs from the MPI Grand Ensemble , also using MPI-ESM-LR and running from 1850 to 2014, are used to provide independent long-term realisations of internal decadal variability, and to assess the impact of initialisation. Results were not found to be sensitive to the time period of the historical simulations (not shown) and so the full period is used.

MPI-ESM-LR simulations are compared to the ERA5 reanalysis for all fields, the HadISST1 (HadISST; ) dataset for SSTs, the HadSLP2 (HadSLP; ) dataset for mean sea level pressure (MSLP), and the NOAA 20th Century Reanalysis version 3 (NOAA 20CR; ) for geopotential height. NOAA 20CR is forced by HadISST data and assimilates surface pressure observations. For ERA5, only data from the hindcast period is used in order to aid comparison with the hindcasts, and because this still covers most of the ERA5 period (1961–2023 instead of 1940–2023). HadISST data extends from 1870 to 2023, and both the full period and hindcast period are analysed. HadSLP data extends from 1850 to 2012, and the periods common to HadSLP and HadISST (i.e. 1870–2012) and common to HadSLP and the hindcasts (1961–2012) are analysed. NOAA 20CR data extends from 1806 to 2015, and the periods common to NOAA 20CR and HadISST (1870–2015) and common to NOAA 20CR and the hindcasts (1961–2015) are analysed. The longer datasets allow us to understand the longer term behaviour of observations/reanalysis, and we include those datasets over the period common with the hindcasts in order to understand whether differences compared to MPI-ESM-LR simulations and ERA5 are due to the longer period or the difference in dataset. We acknowledge that the earlier end dates for HadSLP and NOAA 20CR are a limitation in this study. Note that with respect to the hindcasts, the given time periods refer to the target year, rather than the initialisation year. Hindcast results use all initialisations except where correlated or composited with a variable from reanalysis/observations, in which case only initialisations are used which have target years within the period of the relevant reanalysis/observational dataset.

Throughout this study, all fields are taken as June–August (JJA) means. For all variables and datasets, 7 year means are taken unless otherwise stated. An AMV index is defined as the area-weighted average SST anomaly (relative to the climatology over the full period analysed) between 0–60° N and 280–360° E; this index and similar box-average indices are commonly used to define AMV . Positive and negative phases of the AMV are defined as when the AMV index is greater or less than 0, respectively; results are insensitive to the choice of threshold (not shown). Tropical AMV and Extratropical AMV indices are defined using the part of the AMV region south and north of 30° N respectively. Throughout this study, impacts of AMV are studied through composites of summers with a negative AMV index subtracted from those with a positive AMV index. Therefore, the results shown reflect how positive AMV summers differ from negative AMV summers, and for simplicity the text of this paper will generally refer to the conditions during positive AMV events. However, no robust asymmetries between the phases were found (not shown) and so it is appropriate to reverse the results when considering impacts of the negative phase.

The SST variability is dominated by the anthropogenic forced trend, which cannot be expected to lead to the same atmospheric response as regionally constrained North Atlantic SST variability. Therefore, it is desirable to remove the globally coherent forced trend. The use of a single model large ensemble of historical simulations allows for the externally forced trend to be removed, by regressing out co-variability with the ensemble mean Global Mean SST (GMSST; ). This method is intended for use on both observational and model data, and is applied here for all datasets, with the ensemble mean GMSST timeseries extended beyond the end of the historical period (1850–2014) using future simulations from MPI-ESM-LR under the SSP245 scenario where necessary. GMSST has been calculated as the area-weighted average SST between 60° S and 60° N. Although this method was developed in for the specific purpose of AMV, it is equally applicable to other variables and so it is used consistently in this study.

In the study of decadal variability and when taking rolling means, it is clear that consecutive summers are not independent and that their interdependence cannot be neglected when estimating statistical significance. To calculate statistical significance of skill maps, an existing method to calculate “effective sample size” is used in order to estimate degrees of freedom . Autocorrelations with successive lags are used in this method and several others used to calculate effective sample size (e.g. ), but with increased lag time, autocorrelation values are increasingly uncertain. This method reduces the series of autocorrelation values used to a single parameter α, where the timeseries is assumed to be a sample of an AR(1) process defined by α, with α computed by minimising the mean square error between theoretical AR(1) and sample autocorrelations, where the errors are inversely weighted by the autocorrelation lag. Details of the implementation in this study can be found in the Supplement.

The most prominent surface feature in the summer atmospheric response to AMV found in is a negative pressure anomaly over the North Atlantic centred west of Great Britain and Ireland, which is consistent with simple linear theory for the atmospheric response to extratropical diabatic heating . This is also the main feature of the “East Atlantic Pattern” mode of variability in the North Atlantic, including during summer . For this reason, we define East Atlantic (EA) MSLP as the area-weighted mean MSLP anomaly between 45–60° N and 330–350° E. This region is shown in Fig. c and has been chosen to maximize the observed (HadSLP and ERA5) decadal response to AMV. The same region is also used to define East Atlantic 200 hPa geopotential height anomalies. The results were found to have minimal sensitivity to the box definition (not shown).

Where regression slopes are computed, they are computed across time. For the hindcasts, each time point is a hindcast from a different initialisation year.

Signal-to-noise errors associated with the signal-to-noise paradox are typically diagnosed using the “Ratio of Predictable Components” (RPC; ) metric, defined in as: 1RPC=rmormm where rmo is the correlation between the ensemble mean and observations (i.e. the correlation skill), and rmm is the mean correlation between the ensemble mean and individual ensemble members. This quantity should ideally be one, but underestimated predictable signals or overestimated noise variability will lead to values greater than one. In this study, the quantity rmi is defined as the correlation between the ensemble mean and an individual ensemble member i, so that rmm is the mean of rmi for all members.

Individual summers include both interannual and longer timescale variability. To understand the role that interannual variability plays, it is useful to filter low frequency variability out. We define year-on-year variability as half of the difference between successive summers. This simple high-pass filter damps the low frequency contribution to interannual variability . This method utilises the fact that for a component of variability with a period much longer than a year, there is very little variation between consecutive years, meaning that this difference approximately removes this component. For “true” interannual variability with no autocorrelation between years, the raw difference between years has double the standard deviation, hence need to half the result. When applying this method to hindcasts, successive summers are taken to be at the same lead but with initialisations separated by one year: results are qualitatively the same using differences from the same initialisation separated by a year of lead time.

Where rolling multi-year means are computed, it is expected that the standard deviation of a timeseries will reduce more slowly with rolling window length L when decadal variability contributes more to the overall variability for a particular dataset or variable. It is therefore also useful to understand how the standard deviation would vary with rolling window length under the assumption of white noise, i.e. there is no autocorrelation between years. The rolling mean then becomes a mean of independent variables, for which the standard deviation σ(L) is given by the standard error expression : 2σ(L)=σ(1)L, and therefore the ratio of the rolling mean standard deviation to the single year/season standard deviation is L-1/2 for white noise.

Accurate simulation of SST anomalies associated with AMV are necessary to accurately simulate impacts. Composites differences in positive and negative AMV phase North Atlantic SSTs from different data sources are shown in Fig. . The “horseshoe” pattern of SSTs associated with AMV is clearly present in all observational/reanalysis datasets (Fig. a–c); there is a strong positive signal in the SPG region south of Greenland and a band of positive SST anomalies in the tropical North Atlantic, along with warm anomalies at mid-latitudes in the eastern North Atlantic whilst in the west at mid-latitudes, anomalies are relatively small. The strongest anomalies are in the SPG region and this is particularly true during the hindcast period.

The historical large ensemble shows a similar pattern in composites defined using model AMV (Fig. d), although the SPG response is considerably weaker and with the strongest anomalies centred further south and east compared to observations/reanalysis. The large ensemble hindcast (Fig. e) shows a considerably stronger SPG response which is comparable to hindcast period observations/reanalysis, although the tropical signal is weak. This implies that initialisation has constrained the SPG signature of AMV towards that of observations. By using ERA5 to define AMV phases for the hindcast (Fig. f), the predictability of AMV SSTs can be assessed. The strong SPG signal remains, suggesting that it is highly predictable (consistent with previous studies, e.g. ). However, the tropical signal vanishes, suggesting that AMV-driven tropical SST anomalies are poorly predicted at lead 1–7. Figure S1 in the Supplement shows correlation skill maps for hindcast SSTs relative to ERA5 and HadISST, and indicates that prediction skill is highest in the SPG region.

To understand the surface atmospheric response, Fig.  shows composites of MSLP for different AMV phases using different data sources. In HadSLP during both the full period and period common to the hindcasts (Fig. a and b respectively), the strongest response is a negative anomaly west of Great Britain and Ireland, as previously found in . This feature is also present in ERA5 (Fig. c), but a comparable positive anomaly exists to its north, resembling the summertime North Atlantic Oscillation (SNAO; ). In ERA5 and hindcast period HadSLP, there is a distinct band of negative MSLP anomalies in the tropical North Atlantic, which is a typical low level response to positive SST anomalies in the tropics; this response is weaker in the full HadSLP period.

In the historical MPI-ESM-LR large ensemble (Fig. d), the MSLP response to (model) AMV is very different to that of reanalysis/observations. The composite response is negligible in the extratropics where the observed response is strongest. The tropical response is comparable to observations, although it extends further northwards. In the large ensemble hindcast (Fig. e), the tropical response is perhaps weaker than in the uninitialised simulations, but a negative pressure anomaly comparable to that in and Fig. a–c is present, although notably weaker than observed. The improved extratropical response compared to the historical ensemble is consistent with the difference in SSTs found in Fig. . When defining based on ERA5 AMV, the hindcast MSLP composite is consistent with the corresponding SST composite: the tropical signal vanishes but the extratropical signal remains: a cyclonic anomaly with a position consistent with observations, indicating the potential for predictability albeit with a model signal which is weaker than observed. The standard deviation of 7 year mean EA MSLP is comparable across all data shown in Fig.  at between 0.6 and 0.7 hPa, indicating that the HadSLP and ERA5 composite responses explain a considerable proportion of the decadal variability in this region. An anticyclonic anomaly to the north of the cyclonic anomaly is present in HadSLP and ERA5, which is not captured by historical and hindcast simulations.

To assess predictability, correlation skill (defined as the Pearson correlation coefficient between the ensemble mean and verifying observations/reanalysis) for hindcast MSLP relative to ERA5 (Fig. a) and HadSLP (Fig. b) was computed. Note that as HadSLP does not extend as far as ERA5 and the hindcasts, the years used in Fig. a and b are not identical, although most of the differences are present when using only the HadSLP/hindcast common period (not shown). The highest skill levels are to be found off the west coast of Europe, where the negative MSLP response to AMV is found. This skill relative to ERA5 is highly significant in some regions. In the western North Atlantic, there are regions of negative skill, which has particularly high magnitude and is significant in ERA5. It is not clear if (and if so, how) this relates to AMV, but the high significance implies potential for predictability, that is nonetheless not realised by the MPI-ESM-LR hindcasts due to model error. In the tropics, MSLP skill is generally lower and differs depending on the observational reference used.

Although the hindcasts are capable of predicting EA MSLP, the response to AMV is nonetheless weak. Fig. a shows the histogram of regression slopes for sampled single member timeseries of EA MSLP with the ERA5 AMV index. Despite considerable spread, the regression slope for ERA5 EA MSLP is more negative/stronger than 99 % of sampled hindcast slopes. An underestimated response to a predictable driver can contribute to the signal-to-noise paradox, which is examined in Fig. b. The correlation between ensemble mean EA MSLP and that of sampled individual members rmi is calculated and plotted as a histogram; the ensemble mean correlation skill rmo computed relative to ERA5 is greater than 99 % of all values of rmi, and the ratio of predictable components (RPC) is above 2, suggesting that the reliability issues which define the signal-to-noise paradox are present with high significance. Finally, Fig. c shows the joint distribution (as a 2-dimensional histogram) of the EA MSLP/ERA5 AMV regression slopes and rmi values. The sloped pattern demonstrates that the two quantities are related, with a correlation of -0.50, demonstrating that the weak atmospheric response to AMV relates to the signal-to-noise paradox for summer decadal prediction. Overall, Fig.  demonstrates that the EA MSLP response to AMV is underestimated in MPI-ESM-LR decadal hindcasts and as a consequence, the ensemble signal-to-noise ratio is significantly lower than that of observations, affecting the reliability of the hindcasts.

The upper tropospheric response to AMV is important for downstream impacts. In Fig. , composites differences of zonally anomalous 200 hPa geopotential height for positive and negative AMV phases are shown for different data sources. The zonal mean is removed as there are large discrepancies between NOAA 20CR and ERA5 in the zonal mean component, particularly in the tropics/subtropics. The cause of this discrepancy is unclear and it was found to not be an artifact of the detrending method used. The atmospheric response to extratropical heating is often shallow . Despite this, the upper tropospheric response in the extratropical eastern Atlantic in NOAA 20CR and ERA5 reanalyses (Fig. a–c) appears to be an extension of the negative response at the surface and considerable negative anomalies exist at levels between the surface and 200 hPa in this region (not shown). In this particular region the reanalysis results were found to be the same when the zonal mean is not removed (not shown). In the tropical/subtropical North Atlantic, the upper level response is positive and hence baroclinic through the troposphere, which is typical in response to tropical SST anomalies.

When using model AMV, model composites (Fig. d–e) are similar to each other and markedly different from reanalysis. The response resembles a Rossby wave train emanating from the Caribbean, leading to a negative response east/south east of Newfoundland and a positive response in approximately the position of the strong negative response in reanalyses. The hindcast response is weaker than in the historical simulations. The hindcast composite using ERA5 AMV phases (Fig. f) shows a weak signal which resembles the reanalysis response in the extratropics. Figure f demonstrated that tropical SSTs are poorly predicted by the hindcasts, which likely explains why the tropical-origin Rossby wave response is not present in Fig. f. The standard deviation of 7 year mean EA 200 hPa geopotential height is between 13 and 14 m for all data in Fig.  except NOAA 20CR for the period common with the hindcasts, which is around 11 m. This indicates that the reanalysis composite responses to AMV explain a large proportion of the variability in this region.

With knowledge of the 200 hPa geopotential height response to AMV found in model experiments, it is useful to re-consider whether the reanalysis responses may also relate to a Rossby wave train from the Caribbean. The response over the Caribbean is similar in reanalyses and model experiments, whilst the extratropical response in reanalyses is likely to at least in-part relate to the surface level response to extratropical diabatic heating. As the hindcast extratropical MSLP response is much weaker than that in observations/reanalyses, it is not surprising that it is less likely to extend to the upper troposphere; furthermore in the case of Fig. f where the confounding effect of tropical SST anomalies is reduced, the pattern is remarkably similar, albeit much weaker, to that in reanalyses. It is therefore hypothesised that the upper tropospheric response in reanalyses is some combination of the Rossby wave train response to tropical SSTs which is evident in the model experiments, and the surface response to diabatic heating in the SPG region extending upwards. This hypothesis is tested in the next section.

Subpolar gyre SST variability is known to have a large multidecadal component associated with AMV , whilst considerable interannual variability exists in tropical Atlantic SSTs . Therefore the relative contributions of the tropics and extratropics to North Atlantic SST variability are likely to depend on the timescale of interest. In Fig. , the ratio of standard deviations of rolling-averaged SSTs to that of interannual SSTs is shown for different rolling window lengths, using the full, tropical and extratropical AMV indices as defined in Sect. . Low-frequency variability beyond that of white noise exists for the full AMV region in all datasets. In all cases, extratropical North Atlantic SSTs have a greater ratio than the full region, and in turn tropical SSTs have a lower ratio than the full region. It should therefore be expected that in both model experiments and reanalyses, the longer the rolling window used, the larger the relative contribution of extratropical SSTs to AMV region variability. As a result, it is expected that the diabatic heating response to extratropical SSTs should play an increasingly important role in the upper level atmospheric response with increasing rolling window length.

The coupling of tropical and extratropical North Atlantic SSTs depends on timescale. Figure  also shows correlations between tropical and extratropical AMV for different rolling window lengths. In all cases, the correlation tends to increase with increasing rolling window length; this may be explained by direct forcing of the tropical Atlantic by the extratropical Atlantic on multidecadal timescales , with remote forcing driving interannual variability (, and references therein). The HadISST and ERA5 correlations are large, demonstrating that the extratropical and tropical SSTs are strongly coupled; this, alongside the relatively short length of data availability, means that it is difficult to separate the effects of tropical and extratropical SSTs by defining composites based on them rather than the full AMV index. In both the historical and hindcast simulations, the tropical-extratropical SST correlations are much lower than in observations, although in both cases the correlation increases with rolling window length as in observations.

The timescale dependence of tropical and extratropical contributions to North Atlantic SST variability implies that the atmospheric circulation is also likely to depend on timescale. Figure  shows the composite difference response of zonally anomalous geopotential height to year-on-year AMV region SST variability. Year-on-year variability is computed as half of the difference between successive summers, in order to filter out multi-year variability (see Sect.  for details). Remarkably, a Rossby wave train response emanating from the Caribbean like that found using 7 year rolling means in model experiments (see Fig. ) is found in all reanalyses and model experiments. This implies that this Rossby wave response is a component of the overall atmospheric response to AMV in reality as well as in model experiments, but it is only the dominant component on the 7 year timescale for the model case. The strength of associated geopotential height anomalies are comparable in all data sources. The zonal mean component was found to be similar amongst reanalyses (not shown), but zonal anomalies are used for consistency with Fig. . For the hindcast, results for both lead 1 only and all individual leads up to lead 15 are shown (Fig. e and f respectively). There are no major differences, demonstrating that this feature of the hindcast atmospheric response to North Atlantic SSTs is not dependent on lead time.

As the 200 hPa geopotential height response to North Atlantic SSTs depends on timescale in reanalyses, it is useful to understand whether the negative response to AMV appears in the model on sufficiently long timescales. Figure  shows the regression slope for EA zonal anomaly 200 hPa geopotential height against the AMV index for different rolling window lengths and using different data sources. Only the 16 extended length ensemble members are considered for the hindcasts, and up to lead year 15 is used; results up to lead year 10 are robust when using the full ensemble (not shown). Consistent with Figs.  and , for single years the slope is positive in ERA5 and NOAA 20CR reanalyses, but becomes increasingly negative with increased rolling window length L. The mean regression slope in historical and hindcast simulations is positive for all rolling window lengths tested (up to 15 years), but in both cases, there is a robust decrease in the regression slope with increased rolling window length, and for all multiyear rolling window lengths, the hindcast slope is significantly lower than that of the historical simulations. By including all leads – for rolling window length L=1, leads 1 to 15 are used, for L=3, leads 1–3, 2–4 up to 13–15 are used, and so on – it is shown that the dependence on rolling window length in the hindcasts is not caused by the inclusion of longer leads with longer rolling windows. Leads 1–L (i.e. the first L summers) are also shown; for L=3 and L=7, the slope is significantly more negative than when considering all leads, demonstrating that the differences are greater at short leads; note that as L tends towards 15, the red squares (lead 1–L) and red circles (all leads) necessarily converge. The y axis limits of Fig.  are chosen to highlight model behaviour; an alternative version showing the full curves for reanalyses can be found in the Supplement (Fig. S2).

Figure  also shows the hindcast regression slopes using ERA5 AMV. This is the component of the response which relates to skilfully predicted AMV SSTs. When considering all leads, the slopes are significantly less than zero for rolling window lengths of 3, 5 and 7 years, whilst the lead 1–L slope is significantly more negative than for all leads for L from 1 to 9. This is consistent with the skilfully predicted SPG SSTs and poorly predicted tropical SSTs demonstrated in Fig. f (and Fig. S1): the response using ERA5 AMV is negative as expected in response to SPG SSTs, and the skill is likely to be highest at short leads.

As the regression slope reduces with increased rolling window length in both hindcasts and historical simulations, it is possible that the model can simulate the upwards extension of the surface level response to extratropical diabatic heating seen in reanalyses, but that it is too weak to play a dominant role in the overall upper tropospheric response to AMV. However, the fact that the regression slope remains positive means that the possibility that the response merely weakens with no opposing mechanism can't be ruled out. The regression slopes using ERA5 AMV allow us to extract the response to extratropical SSTs, exploiting the fact that the (multi-year) SST skill is lower in the tropics. The hindcast regression slope with ERA5 AMV is negative at shorter leads (when skill is highest), suggesting that the model can simulate the response to upper tropospheric response to extratropical diabatic heating seen in reanalyses, but that is extremely weak and so the tropical Rossby wave mechanism plays the dominant role in the response to AMV, even at decadal timescales.

Overall, the observed EA 200 hPa geopotential height response to North Atlantic SST anomalies is positive on interannual timescales, but becomes negative in reanalyses for multiyear windows due the increasing importance of extratropical SSTs relative to tropical SSTs. Due to the weaker/shallower response to extratropical diabatic heating, the hindcast and historical response remains positive for all rolling window lengths considered. However, the hindcast response to the ERA5 AMV index is negative for rolling window lengths up to 9 years, due to skilful prediction of extratropical SSTs at these leads.

The capability of MPI-ESM-LR historical and decadal hindcast simulations at capturing the atmospheric response to Atlantic Multidecadal Variability (AMV) – as well as SST anomalies associated with AMV – was tested. We find that both can capture the typical “horseshoe” pattern of SSTs, but only the hindcasts accurately simulate the strength of subpolar gyre (SPG) SST anomalies. Whilst the SPG response in hindcasts is present when defining composites using ERA5 AMV phases, the tropical SST response largely vanishes, indicating predictability in the extratropics but not in the tropics. The previously reported negative EA MSLP response to AMV during boreal summer was found in observations and reanalyses, which is associated with diabatic heating due to subpolar gyre SST anomalies. This response is not present in the historical simulations, but it is present – although with underestimated amplitude – in the hindcasts, in agreement with the differences in SST anomalies. This response is also found in the hindcasts when using ERA5 AMV phases, suggesting that this response is predictable; the correlation skill between the hindcast ensemble mean and observational references was computed which further demonstrated predictability in the extratropical North Atlantic.

The upper tropospheric (200 hPa) geopotential height response to AMV in MPI-ESM-LR historical and hindcast simulations was also analysed and compared to reanalyses. The negative EA MSLP response was found to extend upwards to this level in reanalyses. Modelled responses are consistent amongst historical and hindcast simulations, and resemble a Rossby wave train emanating from the Caribbean and leading to a positive anomaly in the extratropical eastern North Atlantic. The positive anomalies in the Caribbean which appear to be the origin of the Rossby wave train exist in the reanalyses, leading to the hypothesis that the upper tropospheric reanalysis response to AMV is a combination of the extratropical surface response due to diabatic heating extending upwards, and the tropical-to-extratropical Rossby wave train evident in model simulations.

By varying the number of years used for rolling means, it becomes clear that the relative contribution to AMV SSTs from the extratropics compared to the tropics increases for longer rolling means, indicating a larger proportion of low-frequency variability in the extratropics. As the upper tropospheric response to AMV in reanalyses is hypothesised to consist of two components with one due to tropical SSTs and one due to extratropical SSTs, the 200 hPa geopotential height response is investigated for interannual North Atlantic SST variability. In this case, both the reanalysis and model responses to AMV region SSTs resemble the modelled response to 7 year rolling mean AMV SSTs, highlighting the importance of tropical SST anomalies at shorter timescales, and supporting the hypothesis that the model 7 year Rossby wave response is a component of the reanalysis response. The regression slope of the AMV index on EA 200 hPa geopotential height is calculated for different data sources and rolling window lengths, and a robust reduction in the slope (to negative levels in the case of reanalyses) with increasing rolling window length is found, with a larger reduction in the decadal hindcasts compared to the historical simulations. Furthermore, the predictable part of the hindcast slope (calculated by regressing against ERA5 AMV) is found to have the correct sign for rolling windows lengths from 3 to 9 years. However, this is likely to relate to higher prediction skill for extratropical SSTs compared to tropical SSTs at decadal timescales, and even when using 15 year means the hindcast response to AMV remains positive despite the reduction in slope with increased rolling window length.

The two opposing mechanisms that link summertime AMV index SSTs to East Atlantic 200 hPa geopotential height can be summarised as follows:

A tropical-origin mechanism, in which warm anomalies in the tropical Atlantic lead to rising in the upper troposphere, causing a Rossby wave train from the Caribbean to the extratropical eastern Atlantic, with positive geopotential height anomalies to the west of Great Britain and Ireland. In reanalyses, this dominates on interannual timescales, when tropical SST variability dominates overall North Atlantic SST variability. MPI-ESM-LR hindcasts and historical simulations can simulate this mechanism.